Describe how a screw and nut move in relatively opposite directions.
Describe how a screw and nut move in relatively opposite directions.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![### Mechanics and Machine Design: Belt and Pulley Systems
16. **Describe how a screw and nut move in relatively opposite directions.**
When a screw is rotated, the helically shaped thread engages with the corresponding threads of a nut, causing linear motion of the nut relative to the screw. Specifically, if the screw is held fixed and the nut is turned, the nut will move linearly along the axis of the screw in the direction opposite to the rotation. Conversely, if the nut is fixed and the screw is rotated, the screw itself will move linearly in the opposite direction to its rotational movement.
17. **Use the impending motion of the system to determine which side of the belt will have a higher tension.**
In a belt-driven system, the impending motion refers to the direction in which the belt will start to slip. The side of the belt on which the motion starts to slip will experience higher tension. This is because the belt's tension must overcome the friction between the belt and the pulley on the side where motion is impending. Typically, the side of the belt leaving the driving pulley, known as the tight side, has higher tension, while the side entering the driving pulley, known as the slack side, has lower tension.
18. **Compute the contact angle (beta β) between a belt and its corresponding pulley or cylinder.**
The contact angle \( \beta \) between a belt and its corresponding pulley or cylinder is the angle subtended by the belt segment which is in contact with the pulley. This angle is significant as it affects the amount of frictional grip available for power transmission. It can be calculated by knowing the geometry of the system, usually using the following relation:
\[
\beta = 2 \theta
\]
where \( \theta \) is the half-angle of contact.
19. **Compute the tension differential on either side of the belt or cylinder for both flat and V-belts.**
The tension differential between the tight side (T1) and slack side (T2) of the belt can be evaluated using the Capstan equation for flat belts:
\[
\frac{T1}{T2} = e^{\mu \beta}
\]
where \( \mu \) is the friction coefficient and \( \beta \) is the contact angle (in radians).
For V-belts, which are subjected to additional normal force due to the V-shaped groove](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff12ec146-5781-453b-8388-2e7cc9921f6c%2Ffc099853-fe56-4410-a3c2-e6466bf98649%2Fljbkp0g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Mechanics and Machine Design: Belt and Pulley Systems
16. **Describe how a screw and nut move in relatively opposite directions.**
When a screw is rotated, the helically shaped thread engages with the corresponding threads of a nut, causing linear motion of the nut relative to the screw. Specifically, if the screw is held fixed and the nut is turned, the nut will move linearly along the axis of the screw in the direction opposite to the rotation. Conversely, if the nut is fixed and the screw is rotated, the screw itself will move linearly in the opposite direction to its rotational movement.
17. **Use the impending motion of the system to determine which side of the belt will have a higher tension.**
In a belt-driven system, the impending motion refers to the direction in which the belt will start to slip. The side of the belt on which the motion starts to slip will experience higher tension. This is because the belt's tension must overcome the friction between the belt and the pulley on the side where motion is impending. Typically, the side of the belt leaving the driving pulley, known as the tight side, has higher tension, while the side entering the driving pulley, known as the slack side, has lower tension.
18. **Compute the contact angle (beta β) between a belt and its corresponding pulley or cylinder.**
The contact angle \( \beta \) between a belt and its corresponding pulley or cylinder is the angle subtended by the belt segment which is in contact with the pulley. This angle is significant as it affects the amount of frictional grip available for power transmission. It can be calculated by knowing the geometry of the system, usually using the following relation:
\[
\beta = 2 \theta
\]
where \( \theta \) is the half-angle of contact.
19. **Compute the tension differential on either side of the belt or cylinder for both flat and V-belts.**
The tension differential between the tight side (T1) and slack side (T2) of the belt can be evaluated using the Capstan equation for flat belts:
\[
\frac{T1}{T2} = e^{\mu \beta}
\]
where \( \mu \) is the friction coefficient and \( \beta \) is the contact angle (in radians).
For V-belts, which are subjected to additional normal force due to the V-shaped groove
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